Students are obviously young for the most part, and looking for an exciting neighborhood with lots of other young people and things to do. I would assume they want somewhere affordable and safe too (or their parents do at least :-) ).
A lot of students live in Lincoln Park, mostly those that go to DePaul. It's an expensive area, but has the vibe many are going for. I'd say the majority of college students live in or near Lakeview. It's trendy, has a lot of restaurants and bars, and is safe. It's a little bit more pricey than some other neighborhoods, but it's oriented towards a young crowd and students can definitely find cheaper apartments if they look. Students who go to UIC live in University Village, but to be honest the area is a little bit 'manufactured' for me. UIC is really easy to get to on the train, so there's no reason to limit UIC students to the immediate area (same goes for any school really).